Pauli matrices (a) The Pauli matrices can be considered as operators with respect to an orthonormal basis |0), 1) for a two- dimensional Hilbert space. Express each of the Pauli operators in the outer product notation. (a) Find the eigenvectors, eigenvalues, and diagonal representations of the Pauli matrices X, Y, and Z. (c) Calculate the matrix representation of the tensor products of the Pauli operators X and Z; I and X; X and I. Is the tensor product commutative?
Pauli matrices (a) The Pauli matrices can be considered as operators with respect to an orthonormal basis |0), 1) for a two- dimensional Hilbert space. Express each of the Pauli operators in the outer product notation. (a) Find the eigenvectors, eigenvalues, and diagonal representations of the Pauli matrices X, Y, and Z. (c) Calculate the matrix representation of the tensor products of the Pauli operators X and Z; I and X; X and I. Is the tensor product commutative?
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Transcribed Image Text:Pauli matrices
(a) The Pauli matrices can be considered as operators with respect to an orthonormal basis |0), 1) for a two-
dimensional Hilbert space. Express each of the Pauli operators in the outer product notation.
(a) Find the eigenvectors, eigenvalues, and diagonal representations of the Pauli matrices X, Y, and Z.
(c) Calculate the matrix representation of the tensor products of the Pauli operators
X and Z;
I and X;
X and I.
Is the tensor product commutative?
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